text: Townsend, Holst and Oosterhuis also put forward an alternative hypothesis, considering the augmented emission of electrons by the cathode caused by impact of positive ions. This introduced Townsends second ionisation coefficient' ; the average number of electrons released from a surface by an incident positive ion, according to the following formula:
  These two formulas may be thought as describing limiting cases of the effective behavior of the process: either can be used to describe the same experimental results. Other formulas describing various intermediate behaviors are found in the literature, particularly in reference 1 and citations therein.